Explanation

(d)
Since, given that foci of an ellipse are (2, 2)and$\$(4, 2) major axis is of length$\$10
$\Rightarrow \ 2ae = 2\$…(i)
and $2a = 10\ \Rightarrow \ a = 5$ ...(ii)
From Eqs. (i) and (ii),
$2 \times 5 \times e = 2$
$\Rightarrow \ e = \frac{1}{5}$
$\because\ b^{2} = a^{2}\left( 1 - e^{2} \right)\ \therefore\ b^{2} = 25\left( 1 - \frac{1}{25} \right) = 24$
and centre of an ellipse =mid point of foci =(3, 2)
Equation of an ellipse is
$\frac{(x - 3)^{2}}{25} + \frac{(y - 2)^{2}}{24} = 1$